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Vanishing theorems for compact hessian manifolds

Hirohiko Shima (1986)

Annales de l'institut Fourier

A manifold is said to be Hessian if it admits a flat affine connection D and a Riemannian metric g such that g = D 2 u where u is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.

Volume comparison theorems for manifolds with radial curvature bounded

Jing Mao (2016)

Czechoslovak Mathematical Journal

In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume comparisons...

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